Posted by **Laurey** on Tuesday, February 8, 2011 at 3:48pm.

Which of these relations on {0, 1, 2, 3} are equivalence relations? Justify the relation(s) that are not equivalent.

R1: {(0,0), (1,1), (2,2), (3,3)}

R2: {(0,0), (1,1), (1,3), (2,2), (2,3), (3,1), (3,2), (3,3)}

R3: {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

R1: This relations is equivalent

R2: This relation is equivalent

R3: This relation is not equivalent because:

• It is reflexive because the relation does contains (0,0), (1,1), (2,2), and (3,3).

• It is not symmetric because the relation contains (1,2), but not (2,1).

•This relation is transitive.

I think something is not right. . .Any suggestions? Thanks for any helpful replies!

- Discrete Math -
**Laurey**, Tuesday, February 8, 2011 at 4:00pm
I think I may have found the problem in my thinking:

R2 is not equivalent right? Because it is not transitive.

Justification:

It is reflexive because the relation does contain (0,0), (1,1), (2,2), and (3,3).

It is symmetric because the relation contains (1,3) ⋏ (3,1), and (2,3) ⋏ (3,2)

Though the relation contains (1,3) ⋏ (3,2) it does not have (1,2), which means it is not transitive.

- Discrete Math -
**MathMate**, Tuesday, February 8, 2011 at 9:20pm
R1: This relations is equivalent (agree)

R2 is not equivalent right? Because it is not transitive. (agree)

R3: This relation is not equivalent because the relation contains (1,2), but not (2,1) (agree)

Excellent!

- Discrete Math -
**Laurey**, Tuesday, February 8, 2011 at 11:09pm
Thank you for the reassurance.

- Discrete Math :) -
**MathMate**, Wednesday, February 9, 2011 at 6:45am
Keep up the good work!

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